Question: Simplify; express your answer in exponential form. Assume $k\neq 0, a\neq 0$. $\dfrac{{(k^{-4})^{-1}}}{{(k^{-1}a^{-5})^{2}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${k^{-4}}$ to the exponent ${-1}$ . Now ${-4 \times -1 = 4}$ , so ${(k^{-4})^{-1} = k^{4}}$ In the denominator, we can use the distributive property of exponents. ${(k^{-1}a^{-5})^{2} = (k^{-1})^{2}(a^{-5})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(k^{-4})^{-1}}}{{(k^{-1}a^{-5})^{2}}} = \dfrac{{k^{4}}}{{k^{-2}a^{-10}}}$ Break up the equation by variable and simplify. $\dfrac{{k^{4}}}{{k^{-2}a^{-10}}} = \dfrac{{k^{4}}}{{k^{-2}}} \cdot \dfrac{{1}}{{a^{-10}}} = k^{{4} - {(-2)}} \cdot a^{- {(-10)}} = k^{6}a^{10}$.